Abstract
American Journal of Mathematics, vol. x. No. 2 (Baltimore, January 1888).—In the opening paper (pp. 99-130), entitled “Soluble Quintic Equations with Commensurable Coefficients,” G. P. Young develops at some length the application of his general method, described in vol. vi., to the solution of twenty quintic equations, such as x5 - 10x3 - 20x2 - 1505x - 7412 = 0.—Mr. D. Barcroft discusses (pp. 131-40) forms of nonsingular quintic curves. The subject is profusely illustrated by drawings of 47 curves on twelve large pages (interpolated between pp. 140 and 141).—F. Morley (pp. 141-48) writes on critic centres in cubics.—The expression of syzygies among perpetuants by means of partitions, by Captain P. A. MacMahon, R.A. (pp. 149-68), is a very interesting addition to the author's previous papers on the subject.—The number concludes with three short papers: “Démonstration directe de la formule Jacobienne de la transformation cubique,” by the Abbé Faà de Bruno; note on geometric inferences from algebraic symmetry, by F. Morley; and “Surfaces telles que l'origine se projette sur chaque normale au milieu des centres de courbure principaux” (pp. 175-86), by P. Appell.
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